The towering sky projector has been the astronomical icon of the city since the Hayden Planetarium first opened its Art Deco doors on Oct. 3, 1935. Moving silently under the great green dome, the mysterious, spindly dumbbell offered generations of schoolchildren nothing less than the stars.

''I'll never forget the first time I saw the Zeiss,'' said City Councilman Stanley E. Michels of Manhattan, who was 5 at the time. ''I thought it was a monster, a giant praying mantis. Forget about the stars in the dome -- I could have looked forever at the projector.''

But now, for the first time, it will be a street-smart Zeiss. New York's planetarium planners ordered up a $3.5 million star projector to adorn the $210 million Rose Center for Earth and Space when it opens early next year. And the manufacturer, Carl Zeiss of Jena, Germany, found itself coping with a whole lot of city attitude.

Such demands. The New Yorkers insisted on their own color for the projector (black, instead of official corporate Zeiss sky blue). They spurned Zeiss's standard-issue dome interior paint job for a darker, more Gotham-worthy hue (which is formally designated Planetarium Ultralight Gray). They nixed Zeiss's ho-hum Milky Way until German engineers could find a way to project a more souped-up version of the galaxy. Furthermore, Zeiss's boilerplate drawings of the constellations were deemed unacceptable; a Lower East Side artist was assigned to create new images.

Then, the New Yorkers insisted on new planetary projectors and more deep-sky nebulae. Most surprisingly, they refused to house the new Zeiss in an Imax Theater dome like most of the other new planetariums in the world.

Picky, picky. Just how picky? Well, the off-the-shelf Zeiss Mark VIII model, originally ordered by the planetarium, is now so fully loaded that the German engineers have designated it a wholly new model: the Zeiss Mark IX, the only one in existence.

''We wanted to give New Yorkers the best sky in the whole world,'' said Dr. Neil deGrasse Tyson, director of the planetarium, ''because we owe it to them.'' A diehard New Yorker who grew up in the East Bronx, he went to the Bronx High School of Science and won his Ph.D. from Columbia University after an undergraduate flight to Harvard University.

Dr. Tyson explained that thanks to light pollution and haze, ''New Yorkers don't have that much sky,'' adding: ''They aren't accustomed to looking up, and when they do, they're thinking of tall buildings and not the night sky.''

Three German technicians are tuning up the new projector under the 38-foot-tall dome, nearing the end of their company's long New York ordeal. The machine, which arrived in June, was packed in 14 crates, weighed 4 tons and took two years to design. ''They gave us a hard time,'' acknowledged Ralf Hasse, head of Zeiss's electronics team, ''but you know, in Germany we say, 'The customer is the king.' ''

The 1935 Zeiss tracked the stars mechanically from its single motor, ''like a Swiss watch,'' said Dr. Tyson; it was guided by a gearing system controlled by technicians.

The new Zeiss has more than 30 motors controlled by 45 computers. Originally, the stars projected on the ceiling derived from fine holes hand-punched into a copper plate. Now the new 9,100-sun star field is composed of high-intensity white light projected through fiber-optic cables, ''making the stars tinier, brighter, clearer and more realistic,'' said Dr. James S. Sweitzer, special projects director of the planetarium.

He trained for the job of overseeing the new Hayden by spending five years constructing an astronomical observatory in Antarctica. ''That was almost as difficult as building something in Manhattan,'' he said with a laugh.

The stars of the new Zeiss are even equipped with ''scintillation.'' A randomized dimming device recreates the twinkling of starlight shimmering in the earth's turbulent atmosphere.

If the new Zeiss is not as mantislike as its predecessors, the projector is just as distinctive, resembling nothing so much as the bulbous Argus eye of a fly. Thanks to the microelectronic revolution, the new Zeiss has crammed all its goodies under the hood of one projector-studded ''star ball'' instead of the two that visitors remember in the older projectors. The new machine also generates planetary images from a low row of eight boxlike projectors adjacent to the star ball.

The 1930's Zeiss Mark II projector was ultimately replaced at the Hayden by the Zeiss Mark VI projector, which has found a home in Chicago. There, it serves as an organ donor to other still-functioning Mark VI models.

Generations of New Yorkers were imprinted by the earlier Zeisses.

Ellen V. Futter, president of the American Museum of Natural History, the planetarium's parent, was 5 when she first saw the Zeiss. It was during a trip to the Hayden to celebrate her brother's 10th birthday and the projector ''was magical to children because it was where the stars came from,'' she said.

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Dr. Tyson, who had his first experience of the Zeiss on a childhood visit from his home in the Castle Hill section of the Bronx, remembers that the the projector ''looked like a big bug.''

''But I thought the Hayden sky was a hoax, because the sky sure didn't look that way in the Bronx,'' he said.

The planetarium, scheduled to open next February, attracted some 500,000 visitors a year before it was closed for reconstruction in January 1997. The new Zeiss will be augmented by a $4 million ''digital dome'' system. Astronomers from the American Museum and experts from the National Aeronautics and Space Administration have been assembling data from diverse sources to create three-dimensional maps of the Milky Way. The star maps will be used by the system to transport audiences on a visual journey through a 3-D cosmos.

But in housing the Zeiss in its new dome, ''We've gone against fashion and taken the harder way,'' Ms. Futter said, ''to yield a better presentation of the cosmos.'' The museum rejected the recent worldwide trend among planetariums to seat visitors in one direction facing a tipped dome that doubles as a revenue-enhancing Imax screen, capable of attracting audiences to 3-D movies.

''We were strongly against that,'' Dr. Tyson said. ''It would be scientifically inaccurate, and we wanted everyone to have the common view of the center of the room, so they would share the same experience, the feeling of being around a campfire under the night sky.'' Besides, the museum already has its own Imax screen.

Scientific accuracy dictated many of the endless demands made on the Zeiss engineers. For example, the revamped Milky Way is now ''the most detailed planetarium Milky Way in existence,'' Dr. Sweitzer said. Scientific justification also led to the insistence on a new method of projection that allows for the planets to be shown from beyond the solar system.

Accuracy also dictated another Mark IX add-on, enabling the Zeiss to demonstrate precession, the wobble in the earth's axis of rotation, which changes its orientation to the sun over thousands of years.

It was esthetics, though, that dictated the rejection of Zeiss's same-old drawings of the traditional constellations. The planetarium hired a Bowery Street artist, Scott Ewalt, to create new contemporary images of such constellations as Orion, the Swan, the Great Bear and the Lyre.

The jury is still out on the fate of the legendary green arrow. This is, of course, the pointer beamed by the Zeiss mega-flashlight wielded by the godlike astronomical lecturer from his famous console, like a Wizard of Oz conducting the universe with a baton of light.

Currently 29 of the 280 existing Zeiss planetarium projectors are in the United States. Although the Hayden was the fourth American planetarium to land a Zeiss in the 1930's, its prominence and Gotham location gave it status as America's planetarium. Starting in the 1940's, the Post Office regularly delivered to the institution many letters from abroad cryptically addressed ''Planetarium, USA.''

In recent weeks the construction of the Zeiss has been ''an interesting puzzle,'' the 44-year-old Mr. Hasse from Jena said. The Germans toil from 3 P.M. -- when construction workers wind up the day's efforts on the new dome -- till midnight.

After investing so many hours in the Zeiss, can the technicians still muster any sense of wonder at the night sky? ''Nature is better in here,'' said Ulrich Frommhold, a 52-year-old engineer, explaining: ''There are no clouds, there's no light pollution. And do you know? You can see the stars 24 hours a day.''

Indeed, no matter how many bells and whistles the planetarium designers impose on the Zeiss, it all comes down to the star field. ''We have a saying,'' Dr. Sweitzer, 48, said: ''It's the stars, stupid. You can never lose sight of that golden moment when the sun sets and the stars come out. Then the dome disappears and suddenly you're in a limitless expanse.''